Phase diagrams of two-lane driven diffusive systems

Martin Evans, Y. Kafri, K. E. P. Sugden, J. Tailleur

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis of mean-field profiles as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane, an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an 'extremal current principle' for the total current in the two lanes. We also point to classes of models where the analysis fails due to the lack of a dynamically stable current-density relation.

Original languageEnglish
Article numberP06009
Pages (from-to)-
Number of pages25
Journal Journal of Statistical Mechanics: Theory and Experiment
DOIs
Publication statusPublished - Jun 2011

Keywords

  • phase diagrams (theory)
  • driven diffusive systems (theory)
  • stochastic processes (theory)
  • ASYMMETRIC EXCLUSION MODEL
  • OPEN BOUNDARIES
  • STEADY-STATES
  • TRANSITIONS
  • DYNAMICS
  • MOTORS
  • JAMS

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